178 ON THE GOLOUES OF THICK PLATES.
H and x vary together, and after differentiation putting all (h 4- c)'1 for #, we find
and since, according to the definition of ft, X"1^ = /rT'cfe, we have
When c = h the bands are straight, and of uniform breadth, that breadth being equal to ft ; and when the bands are not very much curved ft may still be taken as a convenient measure of the scale of the system; but the formula (25) is not meant to be applied to cases in which the projection of the image of the luminous point falls at all near the centre of the circles.
Rings formed ly a curved mirror, and mewed directly ly the eye, when the luminous point and its image are not in the same plane perpendicular to the axis.
18. The rings and bands of which the theory has been considered in the two preceding sections may be regarded as forming the two extreme cases of the general system. In the first case, the rings appear to have a definite position in space; in the second case, everything depends upon the position of the eye. These are the cases of most interest, but there are some properties of the general system which deserve notice.
In order that rings may be thrown on a screen, it is necessary that the retardation of one of the interfering streams relatively to the other should be sensibly constant over the whole of the dimmed surface, or at least over a large portion of it. But when the rings are viewed directly by the eye, we are concerned with so small a portion of the dimmed surface, in viewing a given point of a ring, that the rings may be seen very well in cases in which they could not be thrown on a screen. Moreover, we have seen that even independently of the small size of the pupil, a portion at least of the system is seen distinctly when the image of the